Theorem 9.5 (Łojasiewicz's inequality [1]}) 
Let \(U\subset \mathbb {R}^d\)  be open, let \(\phi \colon U \rightarrow \mathbb {R}\)  be real analytic and let \(K\subset \mathbb {R}^d\)  be compact. Then there exists a constant \(C>0\)  so that for each \(z\in K\) , we have
\(|\phi (z)| \ge C^{-1}\cdot {\rm dist}(z, Z(\phi ))^{C}.\) 

